Section 3.5 Part 3: Translating Phrases to Algebraic Equations with Integers and Solving

Translate and solve: The number 117 is the product of −13 and z.

ANSWER z=-9 write out and solve the problem ***117 =(-13z)

Translate the word phrase into an algebraic equation and solve: the product of z and −10 gives −80.

ANSWER z=8 The key word product tells us to multiply, while the word gives implies an equals sign. So, the product of z and -10 gives -80 can be written as −10z=−80. To isolate z we need to undo the multiplication. Divide each side by −10 and simplify to find −10z=−80 -10z/-10= -80/-10 z=8

Translate the word phrase into an algebraic equation and solve: twenty-eight subtracted from a gives −24.

a=4 The phrase subtracted from tells us to take the second number away from the first. We must be careful to get the order correct. So, the phrase twenty-eight subtracted from a ***means a−28.The key word gives means "equals" so the entire phrase, twenty-eight subtracted from a gives -24, translates to the equation a−28=−24. To solve an equation, we must isolate the variable. To isolate a we will add 28 to both sides and simplify.

Translate the word phrase into an algebraic equation and solve: the difference of c and twenty-eight is −9.

c=19 write out/solve the problem*** c−28=−9.

Translate the word phrase into an algebraic equation and solve: the product of n and twenty-one is equal to −126.

n=-6 The key word product tells us to multiply and the phrase is equal to implies an equals sign. Then, the entire phrase the product of n and twenty-one is equal to -126 can be translated to 21n=−126. To isolate n we need to undo the multiplication. Divide each side by 21 and simplify to find this answ

Translate into an equation: The difference of p and 2 is −4. Do not solve.

p-2=-4

Translate the word phrase into an algebraic equation and solve: q times −4 gives forty.

q=-10